Planar dielectric waveguide and associated components for integrated circuits

ABSTRACT

A waveguide for sustaining the propagation of electromagnetic energy at frequencies corresponding to the millimeter wave range and through the optical frequency range, i.e. from 30 GHz up to about 106 GHz, and including a dielectric layer mounted atop and substantially coextensive with a ground plane. The waveguide includes at least one metal strip or other waveguiding metal pattern mounted atop the dielectric layer to thereby form a metal-dielectric-ground plane composite structure. The thickness of the dielectric layer is at least greater than 0.1 lambda 0, where lambda 0 is any wavelength within the above specified frequency range, whereby the waveguide structure will not support the TEM or quasi-TEM mode of propagation as characterized by a zero cut-off frequency.

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United Statr Fong [ PLANAR DIELECTRIC WAVEGUIDE AND ASSOCIATED COMPONENTS FOR INTEGRATED CIRCUITS [75] Inventor: Timothy T. Fong, Los Angeles,

Calif.

[73] Assignee: Hughes Aircraft Company, Culver City, Calif.

[ Sept. 2, 1975 Primary ExaminerPaul L. Gensler Attorney, Agent, or FirmWilliam J. Bethurum; W. H. MacAllister 57 ABSTRACT A waveguide for sustaining the propagation of electromagnetic energy at frequencies corresponding to the millimeter wave range and through the optical frequency range, i.e. from 30 GHz up to about 10 GHz, and including a dielectric layer mounted atop and substantially coextensive with a ground plane. The waveguide includes at least one metal strip or other waveguiding metal pattern mounted atop the dielectric layer to thereby form a metal-dielectric-ground plane composite structure. The thickness of the dielectric layer is at least greater than 0.1 A where A is any wavelength within the above specified frequency range, whereby the waveguide structure will not support the TEM or quasi-TEM mode of propagation as characterized by a zero cut-off frequency.

7 Claims, 13 Drawing Figures SHEET 1 BF 3 b/x w 1.0

Fig. 1.

Prior Art SHEET 3 BF 3 Fig. 6b.

Fig.6(1.

Fig.7c1.

Fig. 7b.

Fig. 7c.

PLANAR DIELECTRIC WAVEGUIDE AND ASSOCIATED COMPONENTS FOR INTEGRATED CIRCUITS FIELD OF THE INVENTION This invention relates generally to waveguide structures for sustaining the propagation of millimeter waves and sub-millimeter waves. More particularly, this invention is directed to a planar dielectric waveguide whose geometry is compatible with millimeter wave integrated circuit fabrication.

BACKGROUND Rapid advances in certain solid state components operable at frequencies from 30 GHz through the optical frequency range, i.e. GHz, have made possible many new systems and systems applications in the field of millimeter wave and optical integrated circuits. These solid state components include devices such as IMPAT'T diodes, Gunn diodes, mixers, varactors, detectors, and junction laser devices. Thus, there arises the obvious need for the capability of combining these new components into integrated circuits and systems using low cost lightweight structures which are compatible with the latest state-of-the-art integrated circuit construction techniques.

PRIOR ART The presently used waveguide structure for electrically coupling to the above solid state components and sustaining electromagnetic energy propagation at millimeter and sub-millimeter wave lengths is a so called dielectric waveguide which was originally developed for integrated optics. This dielectric waveguide utilizes a dielectric strip of rectangular cross section which requires precision machining and chemical etching. Such strip is, therefore, very expensive and difficult to fabricate, especially at small geometries. This particular prior art will be discussed in more detail below with reference to FIG. 1c of the drawing. FIGS. la and 1b also depict prior waveguide structures which are similar in their general overall geometry to the present invention. However, the rectangular cross section dielectric waveguide of FIG. 1c is the only prior art capable of operat ing in the above identified frequency range above about GHz with low loss.

THE INVENTION The general purpose of this invention is to provide a new and improved planar dielectric waveguide which is operative at millimeter waves and up through the optical frequency range and which does not require the precise machining and etching steps required in the fabrication of the rectangular dielectric waveguide of FIG. 10. At the same time, the present invention possesses all of the significant advantages of the rectangular dielectric guide in FIG. 10. To attain this purpose, I have discovered that a planar dielectric waveguide comprising a metal-dielectric-ground plane composite structure may be so dimensioned and proportioned relative to the wavelength to be propagated that it will sustain the low loss propagation of electromagnetic energy from millimeter wavelengths through the optical frequency range ie 10 GHZ. Furthermore, this dielectric waveguide will not support the TEM or quasi-TEM mode of propagation as characterized by a zero cutoff frequency. My structure does not require the use of either extremely thin dielectric layers or difficult-to-form dielectric strips of rectangular cross section.

Accordingly, an object of the present invention is provide a new and improved waveguide structure for sustaining electromagnetic wave propagation at millimeter wavelengths and through the optical frequency range.

A further object is to provide a waveguide structure of the type described whose fabrication does not require the machining and etching of strips having a rectangular cross section.

Another object is to provide a waveguide structure of the type described which does not require the formation of extremely thin and difficult to control waveguiding layers.

A feature of this invention is the provision of a waveguide structure which is compatible with the latest state of the art microwave and millimeter wave integrated circuit fabrication techniques.

Another feature of this invention is the provision of a waveguide having a dielectric layer whose thickness is considerably greater than the thickness of conventional microstrip transmission lines. Typically, the thickness of my dielectric layer is 10 to 15 times greater than the dielectric layer thickness of conventional microstrip lines. Consequently, the dominating TEM or quasi-TEM modes are not supported in the planar dielectric waveguide of the present invention.

Another feature is the provision of a planar structure which is adaptive to a wide variety of substrate materials as a result of not requiring etching or machining in its fabrication.

These and other objects and features of the invention will become more fully apparent in the following description of the accompanying drawings.

DRAWING FIG. 1 illustrates, in perspective view, three types of prior art waveguides whose geometries are discussed briefly prior to describing the invention.

FIG. 2a illustrates, in perspective view, the planar dielectric waveguide according to the present invention.

FIG. 2b is a polarization vector graph for the structure in FIG. 2a.

FIG. 3 illustrates, in plan view, a directional coupler utilizing the present invention.

FIG. 4 illustrates, in plan view, a waveguide bend utilizing the present invention.

FIGS. 5a, 5b, and 5c illustrate, in plan view, three different types of resonators utilizing the present invention.

FIGS. 6a and 6b illustrate, in plan view, two different types of power accumulators utilizing the present invention.

FIGS. 7a, 7b, and 7c illustrate, in plan view, three different types of filters utilizing the present invention.

Referring now to FIG. 1, there are shown three prior art waveguide structures whose physical and electrical characteristics will be described in order to facilitate an understanding of the present invention. In FIG. la, there is shown a so-called microstrip line, which is sometimes also referred to as simply a microstrip or microstrip integrated circuit (MIC). This structure includes a planar layer of dielectric material 10 which is deposited on a metal ground plane 12 in a conventional manner. Subsequently, a metal waveguiding strip 14 is deposited on the upper surface of the dielectric layer 10 utilizing conventional metal evaporation and masking techniques. The dielectric layer 10 may typically be fabricated using dielectric materials such as alumina (A1 quartz, teflon and the like. The metal strip 14 and the ground plane 12 may be formed by evaporating gold on the opposing surfaces of the dielectric layer 10. The metal strip I4 will typically be on the order of 600 micrometers in width and one micrometer in thickness. Additionally, the dielectric layer will typically be on the order of 600 micrometers in thickness.

The microstrip transmission line in FIG. la is normally used for propagating microwaves in the TEM mode at frequencies less than about 18 gigahertz. Should one attempt to use the geometry in FIG. In for the TEM mode propagation at higher frequencies, the dielectric layer 10 must be made extremely thin, and the latter presents severe fabrication problems which have never been overcome to produce a commercial device. Thus, as a matter of history, the microstrip transmission line type waveguide in FIG. la has always been used for sustaining the TEM mode of wave propagation at frequencies less than about 18 gigahertz.

In addition to the above characteristics of the microstrip transmission line in FIG. la, the dimension a/b l, and typically the quantity b/ 0.01-0.02, where A is the wavelength of electromagnetic energy propagated in the guide. For this structure, the dominant electromagnetic field polarization vector, E is uniform across the a dimension of the metal waveguide strip I4, and it is also uniform in the vertical or b thickness dimension of the dielectric layer 10.

A structural variation of the microstrip transmission line of FIG. 1a is the so-called wide microstrip or microguidc" structure shown in FIG. 1b. This microguide structure includes a planar dielectric layer 16 mounted on a ground plane 18 in a conventional fashion, and the thickness b of the dielectric layer 16 is the same order of magnitude as the dimension b of the dielectric layer 10 in FIG. la. However, the width a of the metal waveguide strip 20 in FIG. 1b is substantially larger than that of the metal strip 14 in FIG. la, and this microguide structure may be used for operating in the waveguide modes in addition to the TEM modes which propagate in the microstrip structure in FIG. Ia.

In the microguide structure in FIG. lb, the dominant field vector E varies sinusoidally as indicated as a function of the a dimension, and is uniform in the vertical or b dimension of the structure. Typically, the quantity a/b 10-20, whereas the quantity b/A is typically on the order of 0.01-0.02.

The microguide structure in FIG. lb is limited in frequency to about 30 gigahertz and supports either the TEM mode or the waveguide mode of electromagnetic wave propagation. For a further discussion of the elec trical characteristics of the microguide structure in FIG. Ib, reference may be made to an article by Marion E. Hines entitled Reciprocal and Nonreciprocal Modes of Propagation in Ferrite Strip Line and Microstrip Devices, IEEE Transactions on Microwave Theory and Techniques, Volume MIT-l9, No. 5. May 1971, pages 442450 and also to an article by E. G. Cristal et al entitled Microguide-A New Microwave Integrated Circuit Transmission Line" in Dig. Tech. papers, 1972 IEEE GMTT Int. Microwave Symp., pages 212-214.

Referring now to F IG. 10, there is shown a waveguide structure which is generally known in the art as the dielectric waveguide. The dielectric strip 22 of rectangular cross section confines the electromagnetic energy propagated to its own particular cross sectional area, and the layer or strip 22 is mounted on a ground plane 24 as shown. The b dimension of the strip 22 is typically on the order of 5002,000 micrometers. The dielectric waveguide structure in FIG. 1c is normally used for sustaining electromagnetic energy propagation in the hybrid TE or TM mode and at frequencies up to about 10 gigahertz (A 0.3 micrometers). The dominant electromagnetic field polarization vector E varies sinusoidally in relative magnitude as shown across the width a of the dielectric guide and also varies in relative magnitude across the thickness or b dimension of the strip 22 from the point v=0 to the point where v=b, as shown in FIG. 1d. Typically, the parameter a/b for the structure is between approximately I-4 and the parameter b/A is typically on the order of 0.1-0.5.

Now, it will be recalled that to increase the upper frequency limit of the waveguide structures in FIGS. la and lb above, it became necessary to make the dielectric layers in these structures extremely thin. From a commercial device fabrication standpoint, this was impossible to do. Thus, this problem was partially solved by utilizing the rectangular cross section geometry for the dielectric waveguide as shown in FIG. 10. However, the dielectric waveguide strip in FIG. 1c must be fabricated by chemical etching and machining, and this results in undesirable diffraction loss and phase distortion due to the random waveguide variations introduced by the etching and machining processes.

Therefore, the substantial need in the art for a planar waveguide structure with a low diffraction loss, with the capability of sustaining electromagnetic wave propagation out to 10 gigahertz, and with the capability of utilizing high yield planar processing techniques is manifest.

Referring now to the waveguide structure embodying the present invention, there is shown in FIG. 2a a composite waveguide structure including a planar dielectric layer 28 mounted on a supporting ground plane 30. A metal strip guide 32 is deposited as shown on the upper surface of the dielectric layer 28, and the thickness or b dimension of the dielectric layer 28 is considerably greater than the corresponding dimension for the conventional microstrip structures shown in FIGS. 1a and lb. This b dimension for FIG. 2a is typically on the order of ten times the b dimension thickness of the dielectric layers in these two prior art structures in FIGS. Ia and lb, respectively.

The dominant electromagnetic field polarization vector E varies sinusoidally in magnitude as indicated in FIG. 2:: across the width u of the metal strip 32, and the vector E also varies in the vertical or b dimension of layer 28 as indicated by the graph in FIG. 2b. Typically, the parameter a/b for the structure in FIG. 2a is on the order of about I to 4, whereas the parameter b/A is typically in the range of 0. l-l .0. But the number 1.0 in the above typical range is not an upper limitation on the thickness of the dielectric layer 28, and this range can be extended beyond 1.0 as the operating frequency of interest increases, such that a large b dimension can be maintained for ease of fabrication.

The thickness or b dimension of the waveguide layer 28 in FIG. 2a is arrived at by using the Wiener Hopf technique for solving the boundary value problem wherein the reflection coefficient at the open ends of the dielectric guide 28 is first determined. Then, a transverse resonance condition is applied to determine the dispersion relation of the modal field in the layer 28 which in turn determines the required 17 dimension for low loss propagation. The propation constant for the waveguide structure in FIG. 2a was found to be complex; its imaginary part accounts for the edge diffraction loss in the strip through the open ends of the guide. Thus, using this technique it was possible to determine both the dispersion characteristics of the guide and also the small distributed loss inherently associated with an open system.

Unlike the microstrip transmission lines in FIGS. la and 1b above, the transverse dimension b of the guide in FIG. 2a is relatively large compared to the wavelength A Therefore, the waveguide of the present invention does not support the TEM or the quasi-TEM mode of propagation which is characterized by a zero cutoff frequency. Typically, the thickness b in FIG. 2a is ten to fifteen times that of the corresponding thickness dimension I; in FIGS. la and 112 above, so that the dominating TEM or quasi-TEM modes of propagation will not be supported in the waveguide structure FIG. 2a. This results from the strong radiation caused by the relatively large dielectric layer 28 thickness, and the only modes that can still propagate in the dielectric layer 28 are similar to those described by L. A. Vainshtein in Open Resonators For Lasers, Sov Physics JETP, Vol 17, pp 709-719, September 1963. The propagation constants for those latter modes in the transverse a direction are small, and the electromagnetic waves undergo strong reflections at the edges of the overlying metal strip 32. The energy is thus trapped in the waveguide dielectric material beneath strip 32, and there is negligible energy radiated, into free space.

For a more complete discussion of the theory of propagation in the structure of FIG. 2a, reference should be made to an article by T. T. Fong et al incorporated herein by reference and entitled: Planar Dielectric Strip Waveguide for Millimeter Wave Integrated Circuits," published in IEEE Trans. on Microwave Theory and Technique, August, I974. In this publication it is established that if the thickness 12 of the dielectric layer 28 is at least greater than (I. l X A then the above wave propagational characteristics of the waveguide will be provided. On the other hand, the thickness 1) of the dielectric layer 28 may in some cases be equal to l.() A or greater as previously mentioned.

The graph in FIG. 2b shows that the E vector varies in relative magnitude in direction across the thickness or b dimension of the layer 28 from the lower ground plane-dielectric interface 29, where =0, to the dielectricmetal strip interface 3]. where \'=I2.

Referring now to FIGS. 37 in succession, I have disclosed a plurality of waveguide circuit applications for which my invention may be useful and compatible with certain microwave integrated circuit techniques used in forming the particular circuit geometries shown. In FIG. 3 there is shown a directional coupler including a dielectric layer 34 (on a metal ground plane not shown) upon which a first metal strip 36 is positioned closely adjacent to a second, L-shapcd metal strip 38. Electromagnetic energy which is guided beneath the elongated strip 36 may also be coupled through the region 39'of the dielectric layer 34 and into the L-shaped path defined by the metal strip 38.

Alternatively, my invention may be used merely in the construction of simple waveguide bends, such as the waveguide bend defined by the metal strip 40 deposited on the dielectric layer 42 as shown in FIG. 4.

Referring successively now to FIGS. 5a, 5b, and 50, there are shown three different types of resonators which may be fabricated using the present invention. All of these resonators include a similar dielectric layer 44 mounted on a metal ground plane (not shown) and further include, for example, either a rectangular resonator 46, a circular resonator 48 or an annular ring resonator 50 as indicated.

The present invention may also be utilized in the fabrication of a power accumulator, such as those shown in FIGS. 6a and 6b. The power accumulator in FIG. 6a includes, for example, a plurality of IMPATT diodes 52 which are bonded to the dielectric layer 54 and positioned as shown around the periphery of a rectangular resonator 56. Energy from the IMPATT diodes 52 is coupled into the resonator 56 which is tuned to a dominant single frequency. The resonator 56 in turn couples energy at this single frequency through the region 58 of the waveguide dielectric layer 52 and beneath a single strip waveguide member 60 as shown.

Alternatively, a plurality of IMPATF or other suitable avalanche diodes 62 may be mounted as shown on a dielectric layer 64 around the inner periphery of an annular ring resonator 66, as shown in FIG. 61;. The single frequency output signal of the ring resonator 66 may be coupled through the region 68 of the dielectric layer 64 and into (beneath) the output metal waveguide strip 70.

The present invention may also be utilized in the fabrication of millimeter and sub-millimeter wave filters, such as the band pass filter shown in FIG. 7a. This filter includes a common dielectric layer 72 having input and output metal strip waveguide members 74 and 84 between which a plurality of rectangular resonators 76, 78, and 82 are mounted at predetermined spacings as shown. These resonators are characterized by geometries which will provide a desired band pass filter action, as is well known in the art.

Alternatively, the present invention may be utilized in the fabrication of low and high pass filters, such as the filter shown in FIG. 7b. This structure includes a common dielectric layer 86 which supports a single input-output mctalized strip 87, adjacent to which are positioned a plurality of rectangular resonator elements 88.

Finally, the present invention may be utilized in the construction of a channel-dropping filter, such as the filter shown in FIG. 70. This channel-dropping filter includes a common dielectric layer 90 upon which an input strip waveguide member 92 is mounted for receiving signals of frcqucnciesfl /2, /3 andf4. Ring resonators 94 and 96, which are tuned to frequencies fl and f2 respectively, are utilized to couple only frequenciesfl and f2 from the input metal strip waveguide 92 into (beneath) the output metal strip waveguide 98.

Thus, there have been described only some of many waveguide circuit applications in which the present invention may be utilized in the high yield construction of planar dielectric waveguide millimeter wave and sub-millimeter wave integrated circuits.

What is claimed is:

1. A waveguide structure for propagating electromagnetic energy at frequencies corresponding to millimeter waves, sub-millimeter waves and extending to the optical frequency range, including in combination:

a. a ground plane,

b. a layer of dielectric material mounted on said ground plane substantially coextensive therewith,

c. at least one metallic strip member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said strip member; and

d. the thickness of said dielectric layer being at least 0.1 A where M is a wavelength of electromagnetic energy within the above frequency range, whereby the magnitude of the dominant electric field polarizing vector E varies as a function of two dimensions of said dielectric layer, insuring that electromagnetic waves undergo strong reflections at the open ends of said dielectric layer and trapping substantial amounts of energy in said dielectric layer beneath said metal strip.

2. The structure defined in claim 1 wherein the thickness of said layer is between 0.] A and 1.0 A

3. A waveguide structure for propagating electromagnetic energy at frequencies between 30 GHZ and Gl-lz including, in combination:

a. a ground plane,

b. a substantially planar layer of dielectric material mounted on said ground plane and substantially coextensive therewith,

c. at least one metallic member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said metallic member, and

d. said dielectric layer being of at least a thickness equal to 0.1 A where is a wavelength of electromagnetic energy within the above frequency range, whereby relatively thick dielectric layers may be utilized in forming said waveguide without the requirement for machining and etching dielectric strips of a predetermined cross section, and the regions in which electromagnetic energy is propagated within said diclectric layer is controlled by the width of said metallic member and is independent of the cross sectional area of said dielectric layer.

4. The structure defined in claim 3 wherein the thickness of said dielectric layer is between about 0.1 A and l .0 A whereby the dominant electromagnetic field polarizing vector, E varies as a function of two dimensions of said dielectric layer.

5. A waveguide structure for propagating electromagnetic energy at frequencies between 30 GHz and 1O GHz including, in combination:

a. a ground plane,

b. a substantially planar layer of dielectric material mounted on said ground plane and substantially coextensive therewith,

c. at least one metallic member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said metal lic member, and

d. said dielectric layer being of at least a thickness equal to 0.1 A where A is a wavelength of electromagnetic energy within the above frequency range.

6. In a waveguide structure for propagating electromagnetic energy in a layer of dielectric material mounted on a ground plane and being substantially coextensive therewith, and further having at least one metallic strip mounted atop said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said strip, the improvement comprising said dielectric layer having a thickness at least equal to 0.1 A where is a wavelength of electromagnetic energy within a range of frequencies corresponding to the millimeter wave, submillimeter wave and extending to the optical frequency range, whereby the magnitude of the dominant electric field polarizing vector E varies as a function of two dimensions of said dielectric layer, insuring that electromagnetic waves undergo strong reflections at the open ends of said dielectric layer and trapping substantial amounts of energy in said dielectric layer beneath said metal strip.

7. The structure defined in claim 6 wherein the thickness of said dielectric layer is between about 0.1 A and 1.0 A whereby the dominant electromagnetic field polarizing vector, E varies as a function of two dimensions of said dielectric layer. 

1. A waveguide structure for propagating electromagnetic energy at frequencies corresponding to millimeter waves, sub-millimeter waves and extending to the optical frequency range, including in combination: a. a ground plane, b. a layer of dielectric material mounted on said ground plane substantially coextensive therewith, c. at least one metallic strip member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said strip member; and d. the thickness of said dielectric layer being at least 0.1 lambda 0 where lambda 0 is a wavelength of electromagnetic energy within the above frequency range, whereby the magnitude of the dominant electric field polarizing vector Ey varies as a function of two dimensions of said dielectric layer, insuring that electromagnetic waves undergo strong reflections at the open ends of said dielectric layer and trapping substantial amounts of energy in said dielectric layer beneath said metal strip.
 2. The structure defined in claim 1 wherein the thickness of said layer is between 0.1 lambda 0 and 1.0 lambda
 0. 3. A waveguide structure for propagating electromagnetic energy at frequencies betwEen 30 GHz and 106 GHz including, in combination: a. a ground plane, b. a substantially planar layer of dielectric material mounted on said ground plane and substantially coextensive therewith, c. at least one metallic member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said metallic member, and d. said dielectric layer being of at least a thickness equal to 0.1 lambda 0, where lambda 0 is a wavelength of electromagnetic energy within the above frequency range, whereby relatively thick dielectric layers may be utilized in forming said waveguide without the requirement for machining and etching dielectric strips of a predetermined cross section, and the regions in which electromagnetic energy is propagated within said dielectric layer is controlled by the width of said metallic member and is independent of the cross sectional area of said dielectric layer.
 4. The structure defined in claim 3 wherein the thickness of said dielectric layer is between about 0.1 lambda 0 and 1.0 lambda 0, whereby the dominant electromagnetic field polarizing vector, Ey, varies as a function of two dimensions of said dielectric layer.
 5. A waveguide structure for propagating electromagnetic energy at frequencies between 30 GHz and 106 GHz including, in combination: a. a ground plane, b. a substantially planar layer of dielectric material mounted on said ground plane and substantially coextensive therewith, c. at least one metallic member mounted on said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said metallic member, and d. said dielectric layer being of at least a thickness equal to 0.1 lambda 0, where lambda 0 is a wavelength of electromagnetic energy within the above frequency range.
 6. In a waveguide structure for propagating electromagnetic energy in a layer of dielectric material mounted on a ground plane and being substantially coextensive therewith, and further having at least one metallic strip mounted atop said dielectric layer for confining energy propagation in said dielectric layer to regions beneath said strip, the improvement comprising said dielectric layer having a thickness at least equal to 0.1 lambda 0 where lambda 0 is a wavelength of electromagnetic energy within a range of frequencies corresponding to the millimeter wave, submillimeter wave and extending to the optical frequency range, whereby the magnitude of the dominant electric field polarizing vector Ey varies as a function of two dimensions of said dielectric layer, insuring that electromagnetic waves undergo strong reflections at the open ends of said dielectric layer and trapping substantial amounts of energy in said dielectric layer beneath said metal strip.
 7. The structure defined in claim 6 wherein the thickness of said dielectric layer is between about 0.1 lambda 0 and 1.0 lambda 0, whereby the dominant electromagnetic field polarizing vector, Ey, varies as a function of two dimensions of said dielectric layer. 